7.75. The moment generating function of X is given byMX(t)=exp{2e 2} and that of Y by My(t)=(et+)¹0. If X and Y are independent, what are(a) P{X + Y = 2}?(b) P{XY = 0}?(c) E[XY]?

The moment generating function (MGF) of a random variable is:and the MGF of a random variable…

Answered: 7.75. The moment generating function of…

7.75. The moment generating function of X is given by Mx(t) = exp{2et – 2} and that of Y by My(t) (e¹ + 1)¹⁰. If X and Y are independent, what are (a) P{X + Y = 2}? = (b) P{XY = 0}? (c) E[XY]?

Calculus For The Life Sciences

2nd Edition

ISBN:9780321964038

Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Chapter4: Calculating The Derivative

Section4.4: Derivatives Of Exponential Functions

Problem 6E: Find derivatives of the functions defined as follows. y=-4e-0.3x

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Question

7.75. The moment generating function of X is given by
MX(t)
=
exp{2e 2} and that of Y by My(t)
=
(et+)¹0. If X and Y are independent, what are
(a) P{X + Y = 2}?
(b) P{XY = 0}?
(c) E[XY]?

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Step 1: Given information

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Step 2: Identify the distribution of X and Y

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Step 3: Find P{X+Y=2}

Step 4: Find P{XY=0}

Step 5: Find E(XY)

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